Method for predicting a false positive for a radar sensor

ABSTRACT

A simulation method for predicting a false positive for a predefined region outside a desired field of view of a radar sensor. Calculated primary rays having a respective primary energy level represent the radar signal. Reflected rays are calculated based on the primary rays or other reflected rays and based on geometrical data for at least one item within the predefined region. An energy level is determined for each reflected ray based on an estimated reflectivity of the at least one item and based on the primary energy level of the respective primary ray, and a clustering level for the reflected rays is determined based on distances of the respective reflection points. A probability for an occurrence of a false positive is estimated based on the energy level and the clustering level.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority to European Patent Application No.19181196.7, filed on Jun. 19, 2019.

FIELD

The present disclosure relates to a computer implemented method forpredicting a false positive for a radar sensor.

BACKGROUND

Vehicles may comprise radar sensors which are used for monitoring targetobjects within an environment of a vehicle. The radar sensor isconfigured to emit a radar signal in a desired field of view, e.g. infront of the vehicle. In addition, the radar sensor is able to receivereflected signals from the environment of the vehicle, e.g. by antennaswhich are part of the radar sensor. By analyzing the reflected signals,properties of objects within the environment of the vehicle may bedetermined, e.g. the distance and/or the velocity of the objectsrelative to the vehicle comprising the radar sensor.

A portion of the radar signal emitted by the radar sensor may bereflected, however, by parts of the vehicle before arriving at anyobject outside the vehicle in the desired field of view of the radarsensor. For example, a portion of the radar signal may be reflected by apainted bumper being mounted at the front of the vehicle. Therefore, theradar signal may partly leave the desired field of view and enter theinterior of the vehicle. Within the interior of the vehicle, the radarsignal being reflected by e.g. the bumper may be reflected again byparts or items located within the interior of the vehicle and finallyarrive at the antennas of the radar sensor again.

If the part or item within the interior of the vehicle has a highreflectivity for the radar signal, a relatively high amount of energy ofthe radar signal may be detected by the antennas of the radar sensor dueto the multiple reflections of the radar signal within the interior ofthe vehicle. Therefore, the radar sensor may falsely detect an object ata certain distance in front of the vehicle, i.e. at a distance whereactually no real object is located. In other words, the radar sensor maydetect a so-called “false positive” within the desired field of view ofthe radar sensor which is in reality caused by the multiple reflectionsat one or more items or parts within the interior of the vehicle. Sincethe radar sensor detects a non-existing object in such a situation, thefalse positive being due to multiple reflections of a radar signal mayalso be called a “ghost target” or “internal ghost”.

In order to assess the possibility for the occurrence of false positivesor internal ghosts, tests on vehicles have been performed so far.However, these tests are possible only in a very late design stage ofthe vehicle in order to detect false positives in a vehicle which is assimilar as possible to a vehicle being actually delivered to a customer.However, changes in the hardware of the vehicle in order to counteractthe occurrence of false positives are very expensive or even impossiblein a very late stage of the vehicle design. For performing vehicle testsin order to simulate the worst case for the occurrence of falsepositives, the bumper and some parts within the interior of the vehiclemay be covered with foils or paint. This implies an additional effortfor the vehicle tests. In order to keep the effort for the tests withinreasonable limits, no variations are usually considered regarding thematerials of the foils or of the paint.

Accordingly, there is a need for a method being suitable to predict theprobability for an occurrence of a false positive in a predefinedregion, especially in an interior of a vehicle.

SUMMARY

In one aspect, the present disclosure is directed at a computerimplemented method for predicting a false positive for a radar sensoremitting a radar signal in a desired field of view, wherein the falsepositive is to be predicted for a predefined region located outside thedesired field of view. According to the method, geometrical data isreceived for at least one item within the predefined region. A positionof the radar sensor is defined, and a plurality of primary raysrepresenting the radar signal is calculated. Each primary ray has aprimary energy level and originates from the position of the radarsensor. A plurality of reflected rays is calculated based on theplurality of primary rays and based on the geometrical data, whereineach reflected ray originates from a respective reflection point on theat least one item and is a reflection of one of the primary rays or areflection of another reflected ray. Detectable rays are selected fromthe reflected rays, wherein the detectable rays arrive at the positionof the radar sensor. A conductivity of the at least one item isestimated in order to determine a reflectivity of the item based on theconductivity. An energy level is determined for each detectable raybased on the reflectivity of the at least one item and based on therespective primary energy level, and a clustering level for thedetectable rays is determined based on distances of the respectivereflection points of the detectable rays. Finally, a probability for anoccurrence of a false positive is estimated based on the energy leveland the clustering level of the detectable rays.

The predefined region which may cause the false positive for the radarsensor may be an interior or compartment of a vehicle if the radarsensor is installed at a front or a rear of the vehicle, for example.The geometrical data for the at least one item within the predefinedregion may comprise CAD data for the at least one item, e.g. for one ormore parts within an interior of a vehicle. The geometrical data maytherefore comprise realistic construction data e.g. for a vehicle beingavailable in a design stage of the vehicle already.

Instead of performing expensive vehicle tests, the method calculatesrays for simulating a radar signal in order to predict a false positivefor the radar sensor. In addition, the simulation method may be appliedin a very early design stage in which hardware modifications, e.g. of avehicle, can be performed at low cost. As a consequence, the number ofexpensive tests, e.g. at a vehicle in a very late design stage, may beminimized. Therefore, the simulation method for predicting a falsepositive may improve the quality of radar integration in vehicles.Furthermore, the functional safety of the vehicle may be improved due tothe higher quality of radar integration.

The method may comprise one or more of the following features. A subsetof the plurality of reflected rays may be identified based on a maximumnumber of multiple reflections and based on a maximum number of rays foreach number of multiple reflections, and the detectable rays may beselected from the subset of the reflected rays. A respective number ofreflections may be associated to each reflected ray, and a reflected raymay belong to the subset only if its number of reflections is smallerthan or equal to the maximum number of reflections. A respective numberof reflected rays may be counted for each number of multiplereflections, and the subset may be selected from the plurality ofreflected rays such that each number of reflected rays for each numberof multiple reflections is smaller than or equal to the maximum numberof rays for each number of multiple reflections. The subset of theplurality of reflected rays may further be identified by selectingprimary rays and reflected rays having an angle difference beingconstant within a predetermined tolerance such that the primary rays andreflected rays uniformly cover the predefined region.

Furthermore, the method may also comprise one or more of the followingfeatures. The plurality of primary rays may be calculated such that theprimary rays are reflected at a reflector within the desired field ofview of the radar sensor before entering the predefined region. Adistance of at least one predicted false positive with respect to theposition of the radar sensor may be estimated based on the energy leveland the clustering level of the detectable rays if the probability forthe occurrence of a false positive exceeds a predetermined threshold.Estimating the probability for the occurrence of a false positive maycomprise comparing the energy level with an energy threshold beingdependent on a distance from the position of the radar sensor.

Moreover, the method may also comprise one or more of the followingfeatures. The clustering level for the detectable rays may be determinedbased on a number of detectable rays having distances of theirreflection points which are smaller than a predefined distancethreshold. The distance threshold may be dependent on a distance of thereflections points with respect to the position of the radar sensor. Acritical path being related the occurrence of a false positive may beestimated based on the energy level and the clustering level of thedetectable rays. The geometrical data for the at least one item maymodified by a predetermined geometrical tolerance in order to determinemodified geometrical data, and the steps of calculating the plurality ofreflected rays, selecting the detectable rays from the reflected raysand determining energy and clustering levels for the detectable rays maybe repeated based on the modified geometrical data in order to estimatea modified probability for the occurrence of a false positive. Theconductivity of the at least one item may be calculated based on apredefined composition of the at least one item.

According to an embodiment, a subset of the plurality of reflected raysis identified based on a maximum number of multiple reflections andbased on a maximum number of rays for each number of multiplereflections. The detectable rays may be selected from the subset of thereflected rays.

The identification of the subset of the reflected rays may be regardedas “down selection” within the plurality of reflected rays byrestricting the number of multiple reflections and the number of rayswhich are taken into account for the estimation of the probability forthe occurrence of the false positive. Due to this restriction, the timefor performing the method and the required computational effort arestrongly reduced. If the occurrence of a false positive is to bepredicted e.g. for an interior of a vehicle comprising many items havinga complex geometry, the “down selection” for reducing the number ofcalculated rays due to the identification of the subset of a pluralityof reflected rays may be a prerequisite for performing the method withina reasonable time frame at all.

A respective number of reflections may be associated to each reflectedray. A reflected ray may belong to the subset only if its number ofreflections is smaller than or equal to the maximum number ofreflections. The number of reflections to be considered may beapproximately 75. Thus, reflected rays which are the result of manymultiple reflections are neglected by the simulation method since theserays will probably have a very low energy level, or may not addadditional required information for the ghost target risk assessment.

In addition, a respective number of reflected rays may be counted foreach number of multiple reflections. The subset may be selected from theplurality of reflected rays such that each number of reflected rays foreach number multiple reflections is smaller than or equal to the maximumnumber of rays for each number of multiple reflections. That is, therespective number of rays being reflected twice, thrice, four times etc.is restricted to the maximum number of rays. For example, the totalnumber of rays being considered for a double reflection, triplereflection etc. may each be approximately 1500. Due to this restrictionfor the total number of rays to be considered, the computational effortfor the method is decreased again. On the other hand, the maximum numberof rays may be selected to be large enough for covering the predefinedregion properly.

In order to cover the predefined region uniformly by the primary andreflected rays, the subset of the plurality of reflected rays mayfurther be identified by selecting primary rays and reflected rayshaving an angle difference being constant within a predeterminedtolerance. Since the predefined region is uniformly covered due to thesubstantially constant angle difference between the rays, the risk tomiss a false positive within the predefined region is minimized. On theother hand, the computational effort of the method is decreased againsince reflected rays having a very small angle difference may beneglected.

The plurality of primary rays may be calculated such that the primaryrays are reflected at a reflector within the desired field of view ofthe radar sensor before entering the predefined region. The reflectorwithin the desired field of view of the radar sensor may be a bumper ofa vehicle, for example. The rays being reflected by the reflector withinthe desired field of view of the radar sensor may still be regarded asprimary rays when they are entering the predefined region. Since thereflector within the desired field of view may be taken into account bythe simulation method, properties of a “source” for multiple reflectionsof the radar signal may also be considered by the method. Thus, thesimulation method may be suitably adapted to realistic scenarios. Forexample, different materials or paintings and different geometricalproperties of a bumper of a vehicle may be taken into account by themethod in order to minimize the probability for the occurrence of falsepositives.

According to a further embodiment, the distance of at least onepredicted false positive with respect to the position of the radarsensor is estimated based on the energy level and the clustering levelof the detectable rays if the probability for the occurrence of a falsepositive exceeds a predetermined threshold. If a distance of a falsepositive is known, the item or part generating this false positive maybe modified in order to reduce the probability of the occurrence of thefalse positive. For example, geometrical or material properties of theitem or part within the predefined region may be changed in a suitablemanner.

Estimating the probability for the occurrence of a false positive maycomprise that the energy level may be compared with an energy thresholdwhich is additionally dependent on a distance from the position of theradar sensor. In order to estimate the energy level of a detectable ray,the propagation of the electrical field of the radar signal startingfrom the position of the radar sensor may be calculated, and the energylevel may be calculated in a known manner from the electrical field. Bythe comparison of the energy level with an energy threshold for eachdetectable ray relevant rays may be distinguished from rays having a toolow energy level for producing a false positive even if their distancescorrespond to a high clustering level. The dependence of the energythreshold on the distance from the position of the radar sensor mayreflect the propagation of the electrical field within the predefinedregion. In addition, the energy threshold may have a high value for ashort distance from the position of the radar sensor and a lower valuefor larger distances from the position of the radar sensor.

The clustering level for the detectable rays may be determined based ona number of detectable rays having distances of their reflection pointswhich are smaller than a predefined distance threshold. If thepredefined region is an interior of a vehicle, the distance thresholdmay be in a distance of a few millimeters or centimeters. The clusteringlevel of the detectable rays therefore corresponds to a certain numberof rays which have a similar path within the predefined region since thedistances between their reflection points is smaller than the threshold.The number of detectable rays being required for a certain clusteringlevel may be an adjustable parameter for the simulation method. Inaddition, the distance threshold may depend on a distance of thereflection points with respect to the position of the radar sensor. Forexample, the distance threshold may be small for short distances and maybecome larger if the distance from the radar sensor becomes larger aswell.

According to a further embodiment, a critical path being related to theoccurrence of the false positive may be estimated based on the energylevel and the clustering level of the detectable rays. The calculationof the plurality of primary rays and reflected rays allows tracking ofthe rays within the predefined region. Therefore, the method may notonly determine the probability for the occurrence of a false positive,but it may also allow to track the path along which the false positiveis created. The knowledge of the critical path may allow a suitablemodification of the at least one item within the predefined region inorder to minimize the probability for the occurrence of the falsepositive.

The geometrical data for the at least one item may be modified by apredetermined geometrical tolerance in order to determine modifiedgeometrical data. For example, CAD data for an interior of a vehicle mayhave some tolerance which may be taken into account. Based on themodified geometrical data, the steps of the method may be repeated, i.e.calculating the plurality of reflected rays, selecting the detectablerays from the reflected rays and determining energy and clusteringlevels for the detectable rays. Based on these repeated steps of amethod, a modified probability for the occurrence of a false positivemay be estimated. It turned out that the occurrence of false positivesmay be sensitive on slight modifications of the geometry within thepredefined region. In addition, repeating the steps of a method forslightly modified geometrical data may be a check for the stability ofthe simulation method.

In another aspect, the present disclosure is directed at a computersystem, said computer system being configured to carry out several orall steps of the computer implemented method described herein.

The computer system may comprise a processing unit, at least one memoryunit and at least one non-transitory data storage. The non-transitorydata storage and/or the memory unit may comprise a computer program forinstructing the computer to perform several or all steps or aspects ofthe computer implemented method described herein.

In another aspect, the present disclosure is directed at anon-transitory computer readable medium comprising instructions forcarrying out several or all steps or aspects of the computer implementedmethod described herein. The computer readable medium may be configuredas: an optical medium, such as a compact disc (CD) or a digitalversatile disk (DVD); a magnetic medium, such as a hard disk drive(HDD); a solid state drive (SSD); a read only memory (ROM), such as aflash memory; or the like. Furthermore, the computer readable medium maybe configured as a data storage that is accessible via a dataconnection, such as an internet connection. The computer readable mediummay, for example, be an online data repository or a cloud storage.

The present disclosure is also directed at a computer program forinstructing a computer to perform several or all steps or aspects of thecomputer implemented method described herein.

DRAWINGS

Exemplary embodiments and functions of the present disclosure aredescribed herein in conjunction with the following drawings:

FIG. 1 schematically depicts an exemplary vehicle comprising a radarsensor,

FIG. 2 schematically depicts an interior of a radar sensorschematically,

FIG. 3 schematically depicts a calculation of rays for a radar systemwithin a three-dimensional coordinate system,

FIG. 4 schematically depicts a normalized ray energy as a function ofthe distance from the position of a radar sensor, and

FIG. 5 schematically depicts simulation results for the reflectivityover conductivity.

DETAILED DESCRIPTION

FIG. 1 depicts a vehicle 11 comprising a radar sensor 13 for monitoringan environment of the vehicle 11. The radar sensor 13 emits a radarsignal 15 within a desired field of view of the radar sensor 13. If theradar signal 15 is reflected by an object within the desired field ofview, properties of the object can be derived from the reflected radarsignal being detected by the radar sensor 13. For example, the distanceand/or the velocity of the object may be determined relative to thevehicle 11.

The vehicle 11 further comprises a bumper 17 being mounted at the frontof the vehicle 11. The bumper 17 may also be a reflector for the radarsignal 15, i.e. a portion of the radar signal 15 may be reflected by thebumper 17 towards an interior 19 of the vehicle 11. The interior 19 maycomprise an engine compartment and a passenger compartment of thevehicle 11. Furthermore, the interior 19 of the vehicle 11 may beregarded as a predefined region outside the desired field of view of theradar sensor 13. Within this predefined region 19, the radar signal 15being reflected by the bumper 17 may additionally be reflected by one ormore items or parts and eventually detected by the radar sensor 13.

The multiple reflections of the radar signal 15 within the predefinedregion 19, i.e. within the interior 19 of the vehicle 11 outside thedesired field of view of the radar sensor 13, may cause a detection ofan object at a distance or position with respect to the radar sensor 13where actually no real object is located. Such a detection of a “falseobject” due to the multiple reflections may be called “false positive”,“ghost target” or “internal ghost” if the detection is due to multiplereflection within the interior 19 of the vehicle 11.

FIG. 2 is a schematic illustration of the interior of the radar sensor13. In the upper right part of the radar sensor 13, a radar source oremitting device 21 is depicted. In the lower right part, a receivingdevice 23 is shown which comprises for example three radar antennas 25.The emitting device 21 and the receiving 23 are surrounded by a housing27.

The geometrical dimensions and the location of the radar sensor 13 areused as a basis for a simulation method for predicting a false positivecreated by the interior 19 of the vehicle 11 (see FIG. 1 ) according tothe disclosure. As indicated by the structure of the emitting device 21,a full wave simulation is used for the emitting device or radar source21, i.e. a full solution of the Maxwell equations describing theelectrical field of the radar signal. This source could be defined byone or more near field sources or one or more far field sources.Furthermore, the receiving characteristics of the antennas 25 areconsidered as well.

FIG. 3 depicts a result of the computer-implemented method forpredicting a false positive for the radar sensor 13 according to thedisclosure. The radar sensor 13 is positioned at the origin of athree-dimensional coordinate system 31 having an x-axis, a y-axis and az-axis as shown in FIG. 3 . Furthermore, the radar sensor 13 is assumedto be mounted at the front the vehicle 11 (see FIG. 1 ) behind thebumper 17 which is schematically illustrated in FIG. 3 by the curve 33.An item within the interior 19 of the vehicle 11 (see FIG. 1 ) isrepresented by a reflective hollow profile 35 which is also locatedbehind the bumper 17 within the interior 19 of the vehicle.

For the computer-implemented method, CAD data of the reflective hollowprofile 35 is received. In addition, a conductivity of the reflectivehollow profile 35 is estimated as will be explained in detail in contextof FIG. 5 . Based on the conductivity of the reflective hollow profile35, its reflectivity is determined for radar signals being emitted bythe radar sensor 13.

A plurality of primary rays 36 is calculated originating from theposition of the radar sensor 13 and propagating toward the bumper 17within a desired field of view of the radar sensor 13. A portion of theprimary rays 36 is reflected by the bumper 17, i.e. in a region close tothe curve 33 as shown in FIG. 3 . The reflected primary rays 36 arefurther reflected once or multiple times at the structure of thereflective hollow profile 35 at reflection points 38. The reflectionpoints 38 are located at a surface (not shown) of the reflective hollowprofile 35. Therefore, the reflective hollow profile 35 creates aplurality of reflected rays 37.

A portion of the reflected rays 37 may be reflected by the reflectivehollow profile 35 such that these rays arrive at the radar sensor 13again. The reflected rays 37 arriving at the radar sensor 13 may beregarded as detectable rays. If the number of detectable rays and anenergy level of these rays are large enough, a false positive may becreated at the position of the radar sensor 13. That is, due to themultiple reflections of the reflected rays 37 the reflective hollowprofile 35 is detected by the radar sensor 13 as a false object at adistance in front of the bumper 17, i.e. in front of the vehicle 11 (seeFIG. 1 ). In other words, the reflective hollow profile 35 creates falsepositives or internal ghosts for the radar sensor 13.

The calculation of the primary rays 36 and the reflected rays 37 isbased on a simulation method called “shooting and bouncing rays (SBR)”which is usually applied for the simulation of radar cross sectionsoutside of vehicles in very large scale scenarios. This method has notbeen applied so far for the internal reflection of radar signals in avehicle due to the complexity of the calculation for such scenarios. Thecalculation of the rays 36, 37 is based on a radar frequency of 76.5GHz.

In order to perform the method of shooting and bouncing rays (SBR) forthe interior 19 of the vehicle 11 (see FIG. 1 ), a procedure of “downselecting” of the rays 36, 37 is used. In detail, a maximum number ofmultiple reflections being considered is restricted to approximately 75.In addition, the number of rays being considered for each number ofmultiple reflections is restricted to a maximum number, e.g. 1500. Thatis, a maximum of 1500 rays is considered for each of two reflections,three reflections, four reflections, etc. of the primary rays 36.Furthermore, such rays are considered within the simulation method onlywhich have an approximately constant angle difference in order to covera region of interest uniformly. i.e. the predefined region 19. Due tothis “down selection” of the rays 36, 37, the total number of rays whichneed to be considered is reduced approximately by a factor of 1000. Thismakes the method according to the disclosure feasible for realisticscenarios. On the other hand, due to the uniform covering of thepredefined region the risk to miss a false positive is minimized. Inother words, the interior 19 of a vehicle is fully illuminated by therays 36, 37 in spite of the down selection as described above.

According to the method of shooting and bouncing rays (SBR), theelectrical field is also tracked along the rays. Based on the electricalfield, an energy level may be estimated for each of the reflected rays37 arriving at the position of the radar sensor 13. For the calculationof the energy level, the reflectivity of e.g. the reflective hollowprofile 35 is taken into account as explained below in context of FIG. 5. The energy levels of the rays 37 as shown in FIG. 3 are depicted inFIG. 4 as a normalized ray energy in dB over the distance with respectto the position of the radar sensor 13. This distance is shown in mm inFIG. 4 .

In addition, a clustering level is calculated for the rays 36, 37. Assubset of the rays 37 arriving at the radar sensor 13 is regarded as acluster of rays if the reflection points 38 of the rays 37 have distancefrom each other which is smaller than a predefined distance. In otherwords, the rays belonging to a cluster are propagating on almost thesame path. The rays which fulfil this condition, i.e. which arereflected by the reflective hollow profile 35 as a cluster, are depictedin FIG. 4 as clustered rays 43 having star symbols. In contrast, therays 37 which do not fulfil this clustering condition are depicted asminor reflections 39 shown as small circles in FIGS. 3 and 4 .

In order to identify a false positive based on the simulated rays 37,the energy levels of the clustered rays 43 has additionally to beconsidered. For the normalized ray energy, an energy threshold 45 isdefined which is shown in FIG. 4 as a function of the distance withrespect to the position of the radar sensor 13. The energy levels of theclustered rays 43 have to be above the energy threshold 45 in order tobe an indication of a false positive. In FIGS. 3 and 4 , additionalminor reflections 39 are shown which do not fulfil the clusteringcondition as described above although their energy level is partly abovethe energy threshold 45. Therefore, the minor reflections 39 are notconsidered as an indication of a false positive.

Based the clustering level, i.e. the number of rays belonging to eachcluster 43 and based on the energy levels of the rays belonging to therespective cluster a probability for the occurrence of a false positivemay be estimated. As shown in FIG. 4 , the clustered rays 43 surroundedby a respective ellipse 47 provide a strong indication of a falsepositive.

Furthermore, the distances for two false positives or “internal ghosts”with respect to the position of the radar sensor 13 may be derived fromthe clustered rays 43 within the respective ellipse 47 as shown in FIG.4 . Moreover, since the reflected rays 37 are tracked by the simulationmethod as shown in FIG. 3 , a respective critical path can be derivedfrom the illustration as shown in FIG. 3 for the false positives asidentified by the clustered rays 43 within the ellipses 47 as shown inFIG. 4 . The respective critical path may be used e.g. for a new designor a replacement of the reflective hollow profile in an early designstage of the vehicle 11.

In FIG. 5 , the reflectivity in percent is depicted as a function of theconductivity in S/m (Siemens per meter) which may be used for metalparts or bumpers within a vehicle, e.g. the bumper 17 of the vehicle 11(see FIG. 1 ). The curve 51 depicts the theoretical relation betweenreflectivity and conductivity according to the theory of Hagen-Rubens.In addition, two curves 52, 53 are shown which are the result of asimulation by the method for shooting and bouncing rays (SBR) for thereflectivity. The curve 52 represents the average for a triplereflection using a corner reflector, whereas the curve 53 is based on adouble reflection at a metal plate. As can be seen in FIG. 5 , there isa good agreement between the theoretical curve 51 according to theHagen-Rubens relation and the curves 52, 53 for the simulation results.

Moreover, the line 54 represents an average assumed reflectivity of 97%for metal parts, whereas the line 55 represents a reflectivity of 60%which is assumed as a worst case for the reflectivity of the bumper 17.As indicated by the arrow 56, the simulation provides the correctreflectivity of the 97% for a lossy metal having a conductivity of 10⁴S/m. For a lossy material having a conductivity of 5×10¹ S/m which istypically used in a bumper 17, the simulation provides a reflectivity ofapproximately 65% which is in good agreement with the reflectivity of60% assumed as worst case. In summary, the results of FIG. 5 show thatthe theoretical relation according to Hagen-Rubens 51 may be a goodapproximation being used within the simulation method for predictingfalse positives.

The simulation methods as described above may comprise parameters forfine tuning, e.g. the energy threshold 45 as shown in FIG. 4 being afunction of the distance with respect to the position of the radarsensor 13, the predetermined distance for defining the clustering of therays etc. These parameters for fine tuning of the simulation method maybe determined by a comparison with the results of vehicle tests, i.e. bymeasurements within a vehicle comprising the radar sensor 13.

The preceding description is exemplary rather than limiting in nature.Variations and modifications to the disclosed examples may becomeapparent to those skilled in the art that do not necessarily depart fromthe essence of this invention. The scope of legal protection given tothis invention can only be determined by studying the following claims.

I claim:
 1. A computer implemented method for predicting a falsepositive for a radar sensor emitting a radar signal in a desired fieldof view, wherein the false positive is to be predicted for a predefinedregion located outside the desired field of view, the method comprising:receiving geometrical data for at least one item within the predefinedregion, defining a position of the radar sensor, calculating a pluralityof primary rays representing the radar signal, wherein each primary rayhas a primary energy level and originates from the position of the radarsensor, calculating a plurality of reflected rays based on the pluralityof primary rays and based on the geometrical data, wherein eachreflected ray originates from a respective reflection point at the atleast one item and is a reflection of one of the primary rays or areflection of another reflected ray, selecting detectable rays from thereflected rays, wherein the detectable rays arrive at the position ofthe radar sensor, estimating a conductivity of the at least one item inorder to determine a reflectivity of the item based on the conductivity,determining an energy level for each detectable ray based on thereflectivity of the at least one item and based on the primary energylevel of the primary ray that the detectable ray is based on,determining a clustering level for the detectable rays based ondistances of the respective reflection points of the detectable rays,and estimating a probability for an occurrence of a false positive basedon the energy level and the clustering level of the detectable rays. 2.The method according to claim 1, comprising: identifying a subset of theplurality of reflected rays based on a maximum number of multiplereflections and based on a maximum number of rays for each number ofmultiple reflections, and selecting the detectable rays from the subsetof the reflected rays.
 3. The method according to claim 2, wherein arespective number of reflections is associated to each reflected ray anda reflected ray belongs to the subset only if its number of reflectionsis smaller than or equal to the maximum number of reflections.
 4. Themethod according to claim 2, wherein a respective number of reflectedrays is counted for each number of multiple reflections and the subsetis selected from the plurality of reflected rays such that each numberof reflected rays for each number of multiple reflections is smallerthan or equal to the maximum number of rays for each number of multiplereflections.
 5. The method according to claim 2, wherein the subset ofthe plurality of reflected rays is identified by selecting primary raysand reflected rays having a constant angle difference within apredetermined tolerance such that the primary rays and reflected raysuniformly cover the predefined region.
 6. The method according to claim1, wherein the plurality of primary rays is calculated such that theprimary rays are reflected at a reflector within the desired field ofview of the radar sensor before entering the predefined region.
 7. Themethod according to claim 1, wherein a distance of at least onepredicted false positive with respect to the position of the radarsensor is estimated based on the energy level and the clustering levelof the detectable rays if the probability for the occurrence of a falsepositive exceeds a predetermined threshold.
 8. The method according toclaim 1, wherein estimating the probability for the occurrence of afalse positive comprises comparing the energy level with an energythreshold which is dependent on a distance from the position of theradar sensor.
 9. The method according to claim 8, wherein the distancethreshold is dependent on a distance of the reflection points withrespect to the position of the radar sensor.
 10. The method according toclaim 1, wherein the clustering level for the detectable rays isdetermined based on a number of detectable rays having distances oftheir reflection points which are smaller than a predefined distancethreshold.
 11. The method according to claim 1, wherein a critical pathrelated to the occurrence of a false positive is estimated based on theenergy level and the clustering level of the detectable rays.
 12. Themethod according to claim 1, comprising: modifying the geometrical datafor the at least one item by a predetermined geometrical tolerance inorder to determine modified geometrical data, and repeating the steps ofcalculating the plurality of reflected rays, selecting the detectablerays from the reflected rays and determining energy and clusteringlevels for the detectable rays based on the modified geometrical data inorder to estimate a modified probability for the occurrence of a falsepositive.
 13. The method according to claim 1, comprising determiningthe conductivity of the at least one item based on a predefinedcomposition of the at least one item.
 14. A computer system configuredto carry out the computer implemented method of claim
 1. 15. Anon-transitory computer readable medium comprising instructions forcarrying out the computer implemented method of claim 1.